Doing arithmetic by hand: Hand movements during exact arithmetic reveal systematic, dynamic spatial processing

REFERENCES

• Alibali, M. W., Spencer, R. C., Knox, L., & Kita, S. (2011). Spontaneous gestures influence strategy choices in problem solving. Psychological Science, 22, 1138–1144. doi: 10.1177/0956797611417722
   PubMed Web of Science ®Google Scholar
• Anderson, M. L. (2010). Neural reuse: A fundamental organizational principle of the brain. Behavioral and Brain Sciences, 33, 245–313. doi: 10.1017/S0140525X10000853
   PubMed Web of Science ®Google Scholar
• Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68, 255–278. doi: 10.1016/j.jml.2012.11.001
   Web of Science ®Google Scholar
• Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral and Brain Sciences, 22, 577–660.
   PubMed Web of Science ®Google Scholar
• Barsalou, L. W. (2008). Grounded cognition. Annual Review of Psychology, 59, 617–645. doi: 10.1146/annurev.psych.59.103006.093639
   PubMed Web of Science ®Google Scholar
• Beecham, R., Reeve, R. A., & Wilson, S. J. (2009). Spatial representations are specific to different domains of knowledge. PlosOne, 4, 1–5. doi: 10.1371/journal.pone.0005543
   Web of Science ®Google Scholar
• Campbell, J. I. (1994). Architectures for numerical cognition. Cognition, 53, 1–44. doi: 10.1016/0010-0277(94)90075-2
   PubMed Web of Science ®Google Scholar
• Chen, Q ., & Verguts, T. (2012). Spatial intuition in elementary arithmetic: A neurocomputational account. PLoS ONE 7, e31180. doi: 10.1371/journal.pone.0031180
   PubMed Web of Science ®Google Scholar
• Cipora, K., & Nuerk, H. C. (2013). Is the SNARC effect related to the level of mathematics? No systematic relationship observed despite more power, more repetitions, and more direct assessment of arithmetic skill. The Quarterly Journal of Experimental Psychology, 66, 1974–1991. doi: 10.1080/17470218.2013.772215
   Web of Science ®Google Scholar
• Dale, R., Kehoe, C., & Spivey, M. J. (2007). Graded motor responses in the time course of categorizing atypical exemplars. Memory & Cognition, 35, 15–28. doi: 10.3758/BF03195938
   PubMed Web of Science ®Google Scholar
• Dehaene, S. (2003). The neural basis of the Weber–Fechner law: A logarithmic mental number line. Trends in Cognitive Sciences, 7(4), 145–147. doi: 10.1016/S1364-6613(03)00055-X
   PubMed Web of Science ®Google Scholar
• Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 3, 371–396. doi: 10.1037/0096-3445.122.3.371
   Web of Science ®Google Scholar
• Dehaene, S., & Cohen, L. (2007). Cultural recycling of cortical maps. Neuron, 56, 384–398. doi: 10.1016/j.neuron.2007.10.004
   PubMed Web of Science ®Google Scholar
• Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506. doi: 10.1080/02643290244000239
   PubMed Web of Science ®Google Scholar
• Dotan, D., & Dehaene, S. (2013). How do we convert a number into a finger trajectory?. Cognition, 129, 512–529. doi: 10.1016/j.cognition.2013.07.007
   PubMed Web of Science ®Google Scholar
• Dove, G. (2009). Beyond perceptual symbols: A call for representational pluralism. Cognition, 110, 412–431. doi: 10.1016/j.cognition.2008.11.016
   PubMed Web of Science ®Google Scholar
• Fias, W., Brysbaert, M., Geypens, F., & d'Ydewalle, G. (1996). The importance of magnitude information in numerical processing: Evidence from the SNARC effect. Mathematical Cognition, 2(1), 95–110. doi: 10.1080/135467996387552
   Google Scholar
• Fischer, M. H. (2008). Finger counting habits modulate spatial-numerical associations. Cortex, 44(4), 386–392. doi: 10.1016/j.cortex.2007.08.004
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6, 555–556. doi: 10.1038/nn1066
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., Warlop, N., Hill, R. L., & Fias, W. (2004). Oculomotor bias induced by number perception. Experimental Psychology, 51(2), 91–97. doi: 10.1027/1618-3169.51.2.91
   PubMed Web of Science ®Google Scholar
• Freeman, J., Dale, R., & Farmer, T. (2011). Hand in motion reveals mind in motion. Frontiers in Psychology, 2, 59. doi: 10.3389/fpsyg.2011.00059
   PubMed Web of Science ®Google Scholar
• Freeman, J. B., & Ambady, N. (2010). MouseTracker: Software for studying real-time mental processing using a computer mouse-tracking method. Behavior Research Methods, 42, 226–241. doi: 10.3758/BRM.42.1.226
   PubMed Web of Science ®Google Scholar
• Gallese, V., & Lakoff, G. (2005). The brain's concepts: The role of the sensory-motor system in conceptual knowledge. Cognitive Neuropsychology, 22, 455–479. doi: 10.1080/02643290442000310
   PubMed Web of Science ®Google Scholar
• Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345. doi: 10.1037/0033-2909.114.2.345
   PubMed Web of Science ®Google Scholar
• Giaquinto, M. (2007). Visual thinking in mathematics. Oxford: Oxford University Press.
   Google Scholar
• Glenberg, A. M., & Kaschak, M. P. (2002). Grounding language in action. Psychonomic Bulletin & Review, 9(3), 558–565. doi: 10.3758/BF03196313
   PubMed Web of Science ®Google Scholar
• Glenberg, A. M., Sato, M., & Cattaneo, L. (2008). Use-induced motor plasticity affects the processing of abstract and concrete language. Current Biology, 18, R290–R291. doi: 10.1016/j.cub.2008.02.036
   PubMed Web of Science ®Google Scholar
• Goldin-Meadow, S., Cook, S. W., & Mitchell, Z. A. (2009). Gesturing gives children new ideas about math. Psychological Science, 20(3), 267–272. doi: 10.1111/j.1467-9280.2009.02297.x
   PubMed Web of Science ®Google Scholar
• Goldstone, R., Landy, D., & Son, J. Y. (2010). The education of perception. Topics in Cognitive Science, 2, 265–284. doi: 10.1111/j.1756-8765.2009.01055.x
   PubMed Web of Science ®Google Scholar
• Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229. doi: 10.1037/a0027433
   PubMed Web of Science ®Google Scholar
• Hadamard, J. (1954). The psychology of invention in the mathematical field. New York: Dover.
   Google Scholar
• de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110(2), 198–207. doi: 10.1016/j.cognition.2008.11.003
   PubMed Web of Science ®Google Scholar
• Hostetter, A. B., & Alibali, M. W. (2008). Visible embodiment: Gestures as simulated action. Psychonomic Bulletin and Review, 15, 495–514. doi: 10.3758/PBR.15.3.495
   PubMed Web of Science ®Google Scholar
• Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448. doi: 10.1038/nrn1684
   PubMed Web of Science ®Google Scholar
• Hurley, S. L. (2008). The shared circuits model (SCM): How control, mirroring, and simulation can enable imitation, deliberation, and mindreading. Behavioral and Brain Sciences, 31, 1–58. doi: 10.1017/S0140525X07003123
   PubMed Web of Science ®Google Scholar
• Hutchins, E. (2008). The role of cultural practices in the emergence of modern human intelligence. Philosophical Transactions of the Royal Society B: Biological Sciences, 363(1499), 2011–2019. doi: 10.1098/rstb.2008.0003
   PubMed Web of Science ®Google Scholar
• Ito, Y., & Hatta, T. (2004). Spatial structure of quantitative representation of numbers: Evidence from the SNARC effect. Memory & Cognition, 32, 662–673. doi: 10.3758/BF03195857
   PubMed Web of Science ®Google Scholar
• Kaschak, M. P., Madden, C. J., Therriault, D. J., Yaxley, R. H., Aveyard, M. E., Blanchard, A. A., & Zwaan, R. A. (2005). Perception of motion affects language processing. Cognition, 94, B79–B89. doi: 10.1016/j.cognition.2004.06.005
   PubMed Web of Science ®Google Scholar
• Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585. doi: 10.1126/science.1171599
   PubMed Web of Science ®Google Scholar
• Knops, A., Viarouge, A., & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect. Attention, Perception, & Psychophysics, 71, 803–821. doi: 10.3758/APP.71.4.803
   PubMed Web of Science ®Google Scholar
• Knops, A., Zitzmann, S., & McCrink, K. (2013). Examining the presence and determinants of operational momentum in childhood. Frontiers in Psychology, 4, 325. doi: 10.3389/fpsyg.2013.00325
   PubMed Web of Science ®Google Scholar
• Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
   Google Scholar
• Langacker, R. W. (1987). Foundations of cognitive grammar, Vol, 1: Theoretical prerequisites. Stanford, CA: Stanford University Press.
   Google Scholar
• Lindemann, O., Abolafia, J. M., Girardi, G., & Bekkering, H. (2007). Getting a grip on numbers: Numerical magnitude priming in object grasping. Journal of Experimental Psychology: Human Perception and Performance, 33(6), 1400.
   PubMed Web of Science ®Google Scholar
• Loetscher, T., Bockisch, C., Nicholls, M. E. R., & Brugger, P. (2010). Eye position predicts what number you have in mind. Current Biology, 20, R264–R265. doi: 10.1016/j.cub.2010.01.015
   PubMed Web of Science ®Google Scholar
• Loetscher, T., Schwarz, U., Schubiger, M., & Brugger, P. (2008). Head turns bias the brain's random number generator. Current Biology, 18, R60–R62. doi: 10.1016/j.cub.2007.11.015
   PubMed Web of Science ®Google Scholar
• Mahon, B. Z., & Caramazza, A. (2008). A critical look at the embodied cognition hypothesis and a new proposal for grounding conceptual content. Journal of Physiology - Paris, 102, 59–70. doi: 10.1016/j.jphysparis.2008.03.004
   PubMed Web of Science ®Google Scholar
• Marghetis, T. 2014, (in preparation). Bigger, higher, and both: Blended space in mathematical gesture.
   Google Scholar
• Marghetis, T., & Bergen, B. (in press). Embodied meaning, inside and out: The coupling of gesture and mental simulation. In Cornelia Müller, Alan Cienki, Ellen Fricke, Silva H. Ladewig, David McNeill & Sedinha Tessendorf (Eds.), Body-Language-Communication. New York: Mouton de Gruyter.
   Google Scholar
• Marghetis, T., Edwards, L., & Núñez, R. (in press). More than mere handwaving: Gesture and embodiment in expert mathematical proof. In L. Edwards, F. Ferrara, and D. Moore-Russo (Eds.), Emerging perspectives on gesture and embodiment in mathematics. Charlotte, NC: IAP-Information Age Publishing.
   Google Scholar
• Marghetis, T., & Núñez, R. (2013). The motion behind the symbols: A vital role for dynamism in the conceptualization of limits and continuity in expert mathematics. Topics in Cognitive Science, 5, 299–316. doi: 10.1111/tops.12013
   PubMed Web of Science ®Google Scholar
• Matlock, T. (2004). Fictive motion as cognitive simulation. Memory & Cognition, 32, 1389–1400. doi: 10.3758/BF03206329
   PubMed Web of Science ®Google Scholar
• McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception and Psychophysics, 69, 1324–1333. doi: 10.3758/BF03192949
   PubMed Web of Science ®Google Scholar
• McCrink, K., & Wynn, K. (2009). Operational momentum in large-number addition and subtraction by 9-month-olds. Journal of Experimental Child Psychology, 103(4), 400–408. doi: 10.1016/j.jecp.2009.01.013
   PubMed Web of Science ®Google Scholar
• Miles, L. K., Betka, E., Pendry, L. F., & Macrae, C. N. (2010). Mapping temporal constructs: Actions reveal that time is a place. The Quarterly Journal of Experimental Psychology, 63(11), 2113–2119. doi: 10.1080/17470218.2010.524932
   Web of Science ®Google Scholar
• Mix, K. S., & Cheng, Y. L. (2012). The relation between space and math: Developmental and educational implications. Advances in Child Development and Behavior, 42, 197. doi: 10.1016/B978-0-12-394388-0.00006-X
   PubMed Web of Science ®Google Scholar
• Nieder, A., & Miller, E. K. (2003). Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37(1), 149–157. doi: 10.1016/S0896-6273(02)01144-3
   PubMed Web of Science ®Google Scholar
• Núñez, R. (2006). Do real numbers really move? Language, thought, and gesture: The embodied cognitive foundations of mathematics. Reprinted in R. Hersh (Ed.), 18 Unconventional essays on the nature of mathematics (pp. 160–181). New York: Springer.
   Google Scholar
• Núñez, R. (2011). No innate number line in the human brain. Journal of Cross-Cultural Psychology, 45, 651–668. doi: 10.1177/0022022111406097
   Web of Science ®Google Scholar
• Núñez, R., Doan, D., & Nikoulina, A. (2011). Squeezing, striking, and vocalizing: Is number representation fundamentally spatial?. Cognition, 120, 225–235. doi: 10.1016/j.cognition.2011.05.001
   PubMed Web of Science ®Google Scholar
• Núñez, R., & Marghetis, T. (in press). Cognitive linguistics and the concept(s) of number. In R. Cohen-Kadosh and K. Dowker (Eds.), Oxford handbook of numerical cognition. Oxford: Oxford University Press.
   Google Scholar
• Pinhas, M., & Fischer, M. H. (2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109, 408–415. doi: 10.1016/j.cognition.2008.09.003
   PubMed Web of Science ®Google Scholar
• R Development Core Team. (2008). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.R-project.org.
   Google Scholar
• Saygin, A. P., McCullough, S., Alac, M., & Emmorey, K. (2010). Modulation of BOLD response in motion sensitive lateral temporal cortex by real and fictive motion sentences. Journal of Cognitive Neuroscience, 22(11), 2480–2490. doi: 10.1162/jocn.2009.21388
   PubMed Web of Science ®Google Scholar
• Schneider, E., Maruyama, M., Dehaene, S., & Sigman, M. (2012). Eye gaze reveals a fast, parallel extraction of the syntax of arithmetic formulas. Cognition, 125, 475–490. doi: 10.1016/j.cognition.2012.06.015
   PubMed Web of Science ®Google Scholar
• Schwarz, W., & Keus, I. M. (2004). Moving the eyes along the mental number line: Comparing SNARC effects with saccadic and manual responses. Perception & Psychophysics, 66, 651–664. doi: 10.3758/BF03194909
   PubMed Web of Science ®Google Scholar
• Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin & Review, 16, 328–331. doi: 10.3758/PBR.16.2.328
   PubMed Web of Science ®Google Scholar
• Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237–250. doi: 10.1111/1467-9280.02438
   PubMed Web of Science ®Google Scholar
• Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games—but not circular ones—improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101(3), 545. doi: 10.1037/a0014239
   Web of Science ®Google Scholar
• Song, J.-H., & Nakayama, K. (2008). Numeric comparison in a visually-guided manual reaching task. Cognition, 106, 994–1003. doi: 10.1016/j.cognition.2007.03.014
   PubMed Web of Science ®Google Scholar
• Spivey, M. (2007). The continuity of mind. New York: Oxford University Press.
   Google Scholar
• Spivey, M. J., Grosjean, M., & Knoblich, G. (2005). Continuous attraction toward phonological competitors. Proceedings of the National Academy of Sciences of the United States of America, 102, 10393–10398. doi: 10.1073/pnas.0503903102
   PubMed Web of Science ®Google Scholar
• Tzelgov, J., Meyer, J., & Henik, A. (1992). Automatic and intentional processing of numerical information. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18(1), 166.
   Web of Science ®Google Scholar
• Wu, Y. C., & Coulson, S. (2007). How iconic gestures enhance communication: An ERP study. Brain & Language, 101, 234–245. doi: 10.1016/j.bandl.2006.12.003
   PubMed Web of Science ®Google Scholar